Resonator element, resonator, oscillator, electronic apparatus, and moving object

Abstract

A resonator element includes a thick section, a middle section and a thin section, in which at least the thick section performs thickness shear vibration, in which a first step difference is provided at a boundary between the thick section and the middle section, and a second step difference is provided at a boundary between the middle section and the thin section, on one side of a direction of the thickness shear vibration, in which a first antinode of flexural vibration is located between the first step difference and the second step difference, and in which, a distance between the first antinode and the first step difference is indicated by d1, a distance between the first antinode and the second step difference is indicated by d2, and a wavelength of the flexural vibration is indicated by λ, a relationship of 0≦d1≦λ/8 and 0≦d2≦λ/8 is satisfied.

What is claimed is: 
     
       1. A resonator element comprising:
 a thick section; 
 a middle section that is located adjacent to the thick section and is thinner than the thick section; and 
 a thin section that is located around the thick section and the middle section, and is thinner than the middle section, 
 wherein at least the thick section performs thickness shear vibration, 
 wherein a first step difference is provided at a boundary between the thick section and the middle section, and a second step difference is provided at a boundary between the middle section and the thin section, in a direction of the thickness shear vibration, 
 wherein a first antinode of flexural vibration is located between the first step difference and the second step difference, and 
 wherein, when, in the direction of the thickness shear vibration, a distance between the first antinode and the first step difference is indicated by d1, a distance between the first antinode and the second step difference is indicated by d2, and a wavelength of the flexural vibration is indicated by λ, a relationship of 0≦d1≦λ/8 and 0≦d2≦λ/8 is satisfied. 
 
     
     
       2. The resonator element according to  claim 1 , further comprising:
 a vibration portion; 
 a peripheral portion that is thinner than the vibration portion and surrounds the vibration portion; and 
 an excitation electrode that is located on a central portion of the vibration portion in the direction of the thickness shear vibration, 
 wherein the thick section is a region in which the vibration portion overlaps the excitation electrode in a plan view, 
 wherein the middle section is the vibration portion adjacent to the thick section, 
 wherein the thin section is the peripheral portion, and 
 wherein, when a length of the vibration portion in the direction of the thickness shear vibration is indicated by Mx, a relationship of Mx/2=(n/2+1/4)λ+d1+d2 (where n is an integer) is satisfied. 
 
     
     
       3. The resonator element according to  claim 2 ,
 wherein, when a length of the excitation electrode in the direction of the thickness shear vibration is indicated by Ex, a relationship of (Mx−Ex)/2=d1+d2 is satisfied. 
 
     
     
       4. The resonator element according to  claim 1 , further comprising:
 a vibration portion; 
 a peripheral portion that is thinner than the vibration portion and surrounds the vibration portion; and 
 an excitation electrode that overlaps the vibration portion and the peripheral portion in a plan view in the direction of the thickness shear vibration, 
 wherein the thick section is a region in which the vibration portion overlaps the excitation electrode in a plan view, 
 wherein the middle section is a region in which the peripheral portion overlaps the excitation electrode in a plan view, 
 wherein the thin section is the peripheral portion surrounding the excitation electrode in a plan view, and 
 wherein, when a length of the vibration portion in the direction of the thickness shear vibration is indicated by Mx, a relationship of Mx/2=(n/2+1/4)λ+d1+d2 (where n is an integer) is satisfied. 
 
     
     
       5. The resonator element according to  claim 4 ,
 wherein, when a length of the excitation electrode in the direction of the thickness shear vibration is indicated by Ex, a relationship of (Ex−Mx)/2=d1+d2 is satisfied. 
 
     
     
       6. The resonator element according to  claim 4 ,
 wherein the vibration portion includes 
 a first region; and 
 a second region that is thinner than the first region, and is located between the first region and the peripheral portion in at least the direction of the thickness shear vibration in a plan view. 
 
     
     
       7. A resonator comprising:
 the resonator element according to  claim 4 ; and 
 a package in which the resonator element is accommodated. 
 
     
     
       8. A resonator element comprising:
 a thick section; 
 a middle section that is located adjacent to the thick section and is thinner than the thick section; and 
 a thin section that is located around the thick section and the middle section, and is thinner than the middle section, 
 wherein at least the thick section performs thickness shear vibration, 
 wherein a first step difference is provided at a boundary between the thick section and the middle section, and a second step difference is provided at a boundary between the middle section and the thin section, in a direction of the thickness shear vibration, 
 wherein a first antinode and a second antinode, adjacent to each other, of flexural vibration are located between the first step difference and the second step difference, and 
 wherein, when, in the direction of the thickness shear vibration, a distance between the first antinode and the first step difference is indicated by d1, a distance between the second antinode and the second step difference is indicated by d2, and a wavelength of the flexural vibration is indicated by λ, a relationship of 0<d1≦λ/8 and 0<d2≦λ/8 is satisfied. 
 
     
     
       9. The resonator element according to  claim 8 , further comprising:
 a vibration portion; 
 a peripheral portion that is thinner than the vibration portion and surrounds the vibration portion; and 
 an excitation electrode that is located on a central portion of the vibration portion in the direction of the thickness shear vibration, 
 wherein the thick section is a region in which the vibration portion overlaps the excitation electrode in a plan view, 
 wherein the middle section is the vibration portion adjacent to the thick section, 
 wherein the thin section is the peripheral portion, and 
 wherein, when a length of the vibration portion in the direction of the thickness shear vibration is indicated by Mx, a relationship of Mx/2=(n/2+1/4)λ−d1−d2 (where n is an integer) is satisfied. 
 
     
     
       10. The resonator element according to  claim 9 ,
 wherein, when a length of the excitation electrode in the direction of the thickness shear vibration is indicated by Ex, a relationship of (Mx−Ex)/2=λ/2−d1−d2 is satisfied. 
 
     
     
       11. The resonator element according to  claim 8 , further comprising:
 a vibration portion; 
 a peripheral portion that is thinner than the vibration portion and surrounds the vibration portion; and 
 an excitation electrode that overlaps the vibration portion and the peripheral portion in a plan view in the direction of the thickness shear vibration, 
 wherein the thick section is a region in which the vibration portion overlaps the excitation electrode in a plan view, 
 wherein the middle section is a region in which the peripheral portion overlaps the excitation electrode in a plan view, 
 wherein the thin section is the peripheral portion surrounding the excitation electrode in a plan view, and 
 wherein, when a length of the vibration portion in the direction of the thickness shear vibration is indicated by Mx, a relationship of Mx/2=(n/2+1/4)λ−d1−d2 (where n is an integer) is satisfied. 
 
     
     
       12. The resonator element according to  claim 11 ,
 wherein, when a length of the excitation electrode in the direction of the thickness shear vibration is indicated by Ex, a relationship of (Ex−Mx)/2=λ/2−d1−d2 is satisfied. 
 
     
     
       13. The resonator element according to  claim 11 ,
 wherein the vibration portion includes 
 a first region; and 
 a second region that is thinner than the first region, and is located between the first region and the peripheral portion in at least the direction of the thickness shear vibration in a plan view. 
 
     
     
       14. A resonator comprising:
 the resonator element according to  claim 11 ; and 
 a package in which the resonator element is accommodated. 
 
     
     
       15. A oscillator comprising:
 the resonator element according to  claim 11 ; and 
 a circuit that drives the resonator element. 
 
     
     
       16. An electronic apparatus comprising the resonator element according to  claim 11 . 
     
     
       17. A moving object comprising the resonator element according to  claim 11 . 
     
     
       18. A resonator element comprising:
 a thick section; 
 a middle section that is located adjacent to the thick section and is thinner than the thick section; and 
 a thin section that is located around the thick section and the middle section, and is thinner than the middle section, 
 wherein at least the thick section performs thickness shear vibration, 
 wherein a first step difference is provided at a boundary between the thick section and the middle section, and a second step difference is provided at a boundary between the middle section and the thin section, in a direction of the thickness shear vibration, 
 wherein both of the first step difference and the second step difference are located between a first antinode and a second antinode, adjacent to each other, of flexural vibration, and 
 wherein, when, in the direction of the thickness shear vibration, a distance between the first antinode and the first step difference is indicated by d1, a distance between the second antinode and the second step difference is indicated by d2, and a wavelength of the flexural vibration is indicated by λ, a relationship of 0≦d1≦λ/8 and 0≦d2≦λ/8 is satisfied. 
 
     
     
       19. The resonator element according to  claim 18 , further comprising:
 a vibration portion; 
 a peripheral portion that is thinner than the vibration portion and surrounds the vibration portion; and 
 an excitation electrode that is located on a central portion of the vibration portion in the direction of the thickness shear vibration, 
 wherein the thick section is a region in which the vibration portion overlaps the excitation electrode in a plan view, 
 wherein the middle section is the vibration portion adjacent to the thick section, 
 wherein the thin section is the peripheral portion, and 
 wherein, when a length of the vibration portion in the direction of the thickness shear vibration is indicated by Mx, a relationship of Mx/2=(n/2+1/4)λ+d1+d2 (where n is an integer) is satisfied. 
 
     
     
       20. The resonator element according to  claim 19 ,
 wherein, when a length of the excitation electrode in the direction of the thickness shear vibration is indicated by Ex, a relationship of (Mx−Ex)/2=λ/2+d1+d2 is satisfied. 
 
     
     
       21. The resonator element according to  claim 18 , further comprising:
 a vibration portion; 
 a peripheral portion that is thinner than the vibration portion and surrounds the vibration portion; and 
 an excitation electrode that overlaps the vibration portion and the peripheral portion in a plan view in the direction of the thickness shear vibration, 
 wherein the thick section is a region in which the vibration portion overlaps the excitation electrode in a plan view, 
 wherein the middle section is a region in which the peripheral portion overlaps the excitation electrode in a plan view, 
 wherein the thin section is the peripheral portion surrounding the excitation electrode in a plan view, and 
 wherein, when a length of the vibration portion in the direction of the thickness shear vibration is indicated by Mx, a relationship of Mx/2=(n/2+1/4)λ+d1+d2 (where n is an integer) is satisfied. 
 
     
     
       22. The resonator element according to  claim 21 ,
 wherein, when a length of the excitation electrode in the direction of the thickness shear vibration is indicated by Ex, a relationship of (Ex−Mx)/2=λ/2+d1+d2 is satisfied. 
 
     
     
       23. The resonator element according to  claim 21 ,
 wherein the vibration portion includes 
 a first region; and 
 a second region that is thinner than the first region, and is located between the first region and the peripheral portion in at least the direction of the thickness shear vibration in a plan view. 
 
     
     
       24. A resonator comprising:
 the resonator element according to  claim 21 ; and 
 a package in which the resonator element is accommodated.